Question

Find the product of the following binomial: \[\left( x^4 + \frac{2}{x^2} \right)\left( x^4 - \frac{2}{x^2} \right)\]

Answer 1

We will use the identity \[\left( a + b \right)\left( a - b \right) = a^2 - b^2\] in the given expression to find the product.

\[\left( x^4 + \frac{2}{x^2} \right)\left( x^4 - \frac{2}{x^2} \right)\]

\[ = \left( x^4 \right)^2 - \left( \frac{2}{x^2} \right)^2 \]

\[ = x^8 - \frac{4}{x^4}\]